Markov Models for the Performance Analysis of Railway Networks

Authors

C. Schmitz, N. Weik, S. Zieger, N. Nie├čen, A. Schmeink,

Abstract

        In traffic networks like railway lines or roads, capacity is often limited by certain critical areas like junctions or single-tracked sections, which can be seen as servers with multiple queues for jobs arriving from different directions. The behaviour of these servers can be quite complex. For example, it might be possible to process jobs from several queues simultaneously, but not for all possible combinations. Service times can be deterministic or random, and in both cases they might depend on which queue is served, and on some internal state of the server. This work presents an approach to model such a system by Markov chains or Markov processes, with a multi-dimensional state space that is composed of the
number of jobs in each queue, and possibly a finite number of internal states. Apart from the given constraints of the system (e.g. which queues can be served simultaneously), the transitions of the Markov model also describe the chosen service strategy. Thus, it is possible to compare the performance of different service strategies, as well as the performance of different systems (e.g., an existing at-grade junction and a grade separated new version of that junction). The model is tunable to meet different service characteristics and is tested by comparison to simulation.

Keywords

Performance analysis, Markov chain, Markov process, Railway network

BibTEX Reference Entry 

@inproceedings{ScWeZiNiSc17,
	author = {Christoph Schmitz and Norman Weik and Stephan Zieger and Nils Nie{\"s}en and Anke Schmeink},
	title = "{M}arkov Models for the Performance Analysis of Railway Networks",
	pages = "23",
	booktitle = "International Conference on Railway Operations Modelling and Analysis (RailLille)",
	address = {Lille, France},
	month = Apr,
	year = 2017,
	hsb = RWTH-2017-07813,
	}

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